ISTANBUL — President Recep Tayyip Erdogan of Turkey warned Western nations that he would continue to release people who are thought to be members of the Islamic State group and send them back to their home countries if governments continue to pressure Turkey with sanctions. Speaking to reporters Tuesday shortly before leaving Ankara for a visit to the United States, Erdogan was mostly aiming the remarks at the European Union, which has proposed a system for imposing sanctions on Turkey over its unauthorized gas drilling in the eastern Mediterranean. The comments came a day after Turkey said it had begun deporting Islamic State fighters it had captured, starting a program to repatriate the detainees that has strained ties with European countries. Erdogan also took a tough line toward an American detainee who was deported by Turkish authorities Monday and became stranded at the Greek-Turkish border after being turned back by Greek border police. Turkish officials said Monday that the American, who has not been identified, was captured last month in northeastern Syria. “We have started returning Daesh members to their countries and of course there is a serious rush, things are flaring up,” Erdogan told reporters, using the Arabic acronym for the Islamic State. He added that the onus had been on Turkey to handle the exodus of Islamic State fighters from Syria, and that now their home countries must decide what to do. “It does not concern us if they are stuck at the border or not,” Erdogan said, referring to the American detainee. _ Carlotta Gall is a New York Times writer. _